Transitory single line to ground faults are the most frequent type of faults on extra high voltage (EHV) and ultra high voltage (UHV) transmission lines. In prior art systems, when these faults occurred, generally, the three poles of transmission line breakers at each end of the line were opened to clear the primary fault. This type of operation can result in power system instability. The extent of this instability depends on breaker opening time, the system configuration, and various system parameters. However, single phase switching when used in conjunction with a proper compensation apparatus can maintain stability in most cases.
In single phase switching schemes, only the breaker poles at each end of the line associated with the faulted phase are opened for a line to ground fault. The breaker poles associated with the unfaulted phases remain closed. The phase which is opened at both ends to clear a line to ground fault, however, is inductively and capacitively coupled to the unfaulted load-carrying phases energized at a normal system voltage. This coupling, if not compensated, can maintain the secondary arc along the path of the primary fault current and prevent successful reclosing unless the phase is opened for an excessively long interval of time. The secondary arc extinction time depends on variables such as secondary arc current, voltage across the arc path, primary fault current, fault location, arc length, and meterological conditions. Of these variables, the secondary arc current and the voltage across the secondary arc are the most important. These can be reduced by an appropriate compensation apparatus.
One type of compensation apparatus which has been used in single phase switching of transposed lines is illustrated in FIG. 1. It is called a simple four-legged reactor bank. This four-legged reactor bank 10 consists of shunt inductive reactors 12, 14 and 16 which are normally employed on an extra high voltage transmission line for compensation of line capacitance of the phases A, B and C of the line, and an additional reactor 18 which is connected from the neutral of the shunt reactors to ground. Such four-legged reactor banks properly compensate interphase capacitances and phase to ground capacitances of equal magnitude. Methods for calculating the inductance, current ratings and voltage ratings of these inductors are well known in the art.
This compensation apparatus, which is useful for a transposed transmission line, will not generally reduce the secondary arc current sufficiently on long untransposed transmission lines because of unequal line interphase capacitances.
The present inventors, in "Compensation Scheme for Single-Pole Switching on Untransposed Transmission Lines," published in IEEE-Transactions on Apparatus and Systems, Vol. PAS-97, No. 3 (July/August 1978) analysed a modified four-legged reactor bank using four switches whose operations are coordinated with the line breakers. According to this compensation scheme an untransposed transmission line system utilizes a simple four-legged reactor bank to provide sufficient compensation between outer phases of the transmission line, while the modified four-legged reactor bank provides the additional compensation required for the mid-to-outer-phase capacitances.
The principles of operation of this modified four-legged reactor bank are best illustrated in FIG. 2. Referring to FIG. 2b, a center phase fault, consisting of an arc from phase conductor B to ground is shown. A reactor bank 20 in this case is configured in a manner identical to reactor bank 10 of FIG. 1. Provided the inductance values of shunt reactors 22, 24 and 26, and neutral reactor 28 are properly chosen, the secondary arc current I.sub.f will be compensated, that is, reduced to a small value or held to a low enough value that it will be extinguished in a reasonable time with respect to system stability requirements. During this time, the breakers associated with phase B are opened at both ends of the transmission line.
FIGS. 2a and 2c illustrate the configurations of reactor bank 20 necessary to extinguish faults in the form of arcs to ground on phases A and C, the outer phases, respectively. The shunt inductor associated with the unfaulted outer phase, inductor 26 in FIG. 2a, and inductor 22 in FIG. 2c, is switched so that its side opposite the side connected to the unfaulted phase is connected to ground rather than to the ungrounded side of neutral inductor 28. Shunt reactor 24 associated with center phase B and the shunt reactor associated with the faulted phase (inductor 22 in FIG. 2a and inductor 26 in FIG. 2c) are both connected to the ungrounded side of neutral reactor 28. The breakers associated with the faulted phase are opened for a period of time sufficient to extinguish the arc.
FIG. 3 illustrates how four switches 30, 32, 34 and 36 are incorporated into reactor bank 20 to configure reactor bank 20 to clear faults on phases A, B and C. During normal system operation, when no faults exist, switches 30, 32, 34 and 36 remain closed. When a fault occurs on phase B an apparatus for sensing a fault condition on that phase produces a signal which causes switches 34 and 36 to open producing the configuration of FIG. 2b. This signal also causes the line breakers associated with phase B to open.
The apparatus or means for sensing the fault is of a type well known in the art. Generally, it responds to a sudden substantial increase in current on the faulted phase due to the presence of a fault condition as illustrated in FIG. 3a. When a fault occurs on phase A switches 32 and 34 are opened in response to a signal from a means for sensing a fault on phase A. Switches 30 and 36 remain closed. Thus the configuration of FIG. 2a is produced. Line breakers associated with phase A are temporarily opened and the arc is extinguished.
A similar series of events occurs for a fault on phase C, but as will be appreciated by referring to FIG. 3c, in this case switches 30 and 36 are opened while switches 32 and 34 remain closed, producing the configuration of FIG. 2c. Line breakers associated with phase C are now opened and reclosed after a period of time in which the fault is cleared.
For successful simple phase switching the reactive admittance matrix for the simple and switched compensation banks must match the line capacitive admittance matrix. The inventors in the above cited paper have developed expressions for the admittance matrix of the modified or switched four-legged reactor bank for the above configurations and for the equivalent admittances of the transmission line for faults at various locations. The equations needed for simplified secondary arc current calculations are provided and a graphical method of solving for neutral reactor values which limit the maximum steady state secondary arc current to a given value is developed. Using this method, now well known in the art, solutions are expressed in terms of permissible ratios of reactance of the neutral inductor to the reactance of the shunt inductor in the simple four-legged reactor bank and permissible ratio of the reactance of the neutral inductor to the reactance of the shunt inductor in the switched four-legged reactor bank which can be used when a particular permissible ratio in the simple four-legged reactor bank is selected. Alternatively, a particular ratio may be selected for the modified or switched reactor bank, and a permissible ratio for the simple four-legged bank selected. Expression for secondary arc current, neutral reactor voltages and recovery voltages needed to produce a practical system are also computed and plotted.
In "Single-Phase Switching Parameters for Untransposed EHV Transmission Lines" published in IEEE Transactions on Apparatus and Systems, Vol. PAS-98 (March/April 1979), B. R. Shperling and A. Fakheri, two of the present inventors, have outlined the results of calculations following the general method outlined above for using a modified four-legged reactor bank of the type shown in FIG. 3 on a 765 kilovolt untransposed transmission line. The results of these calculations for various transmission lines lengths are disclosed. The various configurations show (1) a modified and simple reactor bank at the transmission line terminals; (2) a modified reactor bank at only one of the line terminals; and (3) three shunt reactor banks at the line terminals.
The length of the transmission line determines which of the above configurations should be used. The ratios of the reactants of the neutral inductor to that of the shunt reactors for each arrangement and for various lengths of transmission lines for arrangements 1 and 2 is plotted as a function of the compensation factor h.sub.g which is defined as the ratio of the reactive component of the shunt reactors (KVA reactive) over the capacitive component of the transmission line (KVA capacitive).
While the system arrangements disclosed in the above mentioned paper are adequate for clearing faults on a large variety of untransposed transmission lines by using single phase switching it will be recognized by one skilled in the art that the nature of the load on a given transmission line varies greatly as the load on that line is changed. For example, during periods of heavy loading the load presented results in a large inductive component in the secondary arc current. This component is greatly reduced under conditions of light loading.
The modified four-legged reactor bank described above must always be connected to the transmission line to extinguish arcs regardless of the condition of the load. Keeping such a reactor on the line permanently results in an uneconomical load distribution in the system. It is required, therefore, in many systems to switch off the shunt reactors during heavy load conditions and, at the same time, have them available for extinguishing the secondary arcs after single phase to ground faults. An extra set of three high voltage breaker switches and associated control circuits are therefore required.